IB Mathematics SL
Internal Assessment
This is a Sample Title
- This is a Sample Subtitle -
By Student Name
Candidate #
October 5, 2016
Contents
1 Introduction
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2 Scoring Criterion
1
2.1
Communication ............................................................................................................................ 1
2.2 Mathematical Presentation......................................................................................................... 2
2.3 Personal Engagement .................................................................................................................. 2
2.4 Reflection ...................................................................................................................................... 3
2.5 Use of Mathematics ..................................................................................................................... 3
3 Conclusion
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4 Using LATEX
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References
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Student Name
Introduction
The internally assessed component in these courses is a mathematical exploration. This is a short
report written by the student based on a topic chosen by him or her, and it should focus on the
mathematics of that particular area. The emphasis is on mathematical communication (including
formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing
and thoughtful reflection. A student should develop his or her own focus, with the teacher providing
feedback via, for example, discussion and interview. This will allow all students to develop an area
of interest for them, without a time constraint as in an examination, and will allow all to experience
a feeling of success. [1]
In addition to testing the objectives of the courses, the exploration is intended to provide students
with opportunities to increase their understanding of mathematical concepts and processes, and
to develop a wider appreciation of mathematics. These are noted in the aims of the courses,
in particular aims 6-9 (applications, technology, moral, social and ethical implications, and the
international dimension). It is intended that, by doing the exploration, students benefit from the
mathematical activities undertaken and find them both stimulating and rewarding. It will enable
students to acquire the attributes of the IB learner profile 1.
2 Scoring Criterion
2.1
Communication
This criterion assesses the organization and coherence of the exploration. A well-organized exploration
includes an introduction, has a rationale (which includes explaining why this topic was chosen),
describes the aim of the exploration and has a conclusion. A coherent exploration is logically
developed and easy to follow. Graphs, tables and diagrams should accompany the work in the
appropriate place and not be attached as appendices to the document.[2]
1An
example footnote
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2.2 Mathematical Presentation
This criterion assesses to what extent the student is able to use appropriate mathematical language
(notation, symbols, terminology), define key terms where required, and use multiple forms of
mathematical representation such as formulae, diagrams, tables (see table 1), charts, graphs and
models, where appropriate.
x
0
1
2
f (x)
3
6
9
Table 1: Caption goes here
Students are expected to use mathematical language when communicating mathematical ideas,
reasoning and findings, where appropriate. Students are encouraged to choose and use appropriate
ICT tools such as graphic display calculators, screenshots, graphing (see figure 1), spreadsheets,
databases, drawing and word-processing software, as appropriate, to enhance mathematical communication.
Figure 1: The Squeeze Theorem
2.3 Personal Engagement
This criterion assesses the extent to which the student engages with the exploration and makes it
their own. Personal engagement may be recognized in different attributes and skills. These include
thinking independently and/or creatively, addressing personal interest and presenting mathematical
ideas in their own way.
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To receive full marks, students must show evidence of outstanding personal engagement. The
work should be original. It may be from historical ideas and real world situations (for example,
socio-economic, political awareness). Students should create some examples or present some ideas
explained in depth.
2.4 Reflection
This criterion assesses how the student reviews, analyses and evaluates the exploration. Although
reflection may be seen in the conclusion to the exploration, it may also be found throughout the
exploration.
Students should ideally have continuous reflection throughout the task, which should include the
following: identify and address issues as the piece develops, discuss limitations of the work where
applicable, provide ideas for extensions, and reflect on the significance of the findings.
2.5
Use of Mathematics
This criterion assesses to what extent and how well students use mathematics in the exploration.
Students are expected to produce work that is commensurate with the level of the course. The
mathematics explored should either be part of the syllabus, or at a similar level or beyond. It should
not be completely based on mathematics listed in the prior learning. If the level of mathematics is
not commensurate with the level of the course, a maximum of two marks can be awarded for this
criterion.
The mathematics can be regarded as correct even if there are occasional minor errors as long as they
do not detract from the flow of the mathematics or lead to an unreasonable outcome. Sophistication
in mathematics may include understanding and use of challenging mathematical concepts, looking
at a problem from different perspectives and seeing underlying structures to link different areas of
mathematics. Rigour involves clarity of logic and language when making mathematical arguments
and calculations. Precise mathematics is error-free and uses an appropriate level of accuracy at all
times.
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3 Conclusion
The exploration is intended to be an opportunity for students to use mathematics to develop an
area of interest to them rather than merely to solve a problem set by someone else. Criterion C
(personal engagement) will be looking at how well the student is able to demonstrate that he or
she has made the exploration their own and expressed ideas in an individual way.
It is difficult to be prescriptive about mathematical writing. However, the Mathematics SL guide
and the Mathematics HL guide state that 6 - 12 pages should be appropriate. A common failing of
mathematical writing is excessive repetition, and this should be avoided, as such explorations will
be penalized for lack of conciseness. However, it is recognized that some explorations will require
the use of several diagrams, which may extend them beyond the page limit.
4 Using LATEX
Be sure to cite any sources you use throughout the text. See the references section in the TEX
file for samples of MLA citations for books[3], articles[4], journals[5], websites[6], and images[7].
Replace “name1”, “name2”, etc. with appropriate keywords. There are more advanced methods
of creating bibliographies, but the method used here is simplest for a short list of references.
Also note that you may have to compile the document twice before you see updated citations and
the updated table of contents.
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References
[1]Alcosser, Howard. “Diamond Bar High School.” Internal Assessment : Mathematical
Exploration. Web. 27 May 2015. <http://dbhs.wvusd.k12.ca.us/ourpages/auto/
2010/10/1/38060822/INTERNAL%20ASSESSMENT handout.pdf>.
[2] Alcosser, Howard. “Diamond Bar High School.” Mathematical Exploration Rubric. Web. 27
May 2015. <http://dbhs.wvusd.k12.ca.us/ourpages/auto/2010/10/1/38060822/
IA 2014 rubric.pdf>.
[3] Lastname, Firstname. Title of Book. City of Publication: Publisher, Year of Publication.
Medium of Publication.
[4] Author(s). “Title of Article.” Title of Periodical Day Month Year: pages. Medium of
publication.
[5] Author(s). “Title of Article.” Title of Journal Volume.Issue (Year): pages. Medium of
publication.
[6] Editor, author, or compiler name (if available). Name of Site. Name of institution or
organization affiliated with the site (sponsor or publisher), date of resource creation (if
available). Medium of publication. Date of access. <http://www.samplewebsite.com>.
[7] Artist’s name, The Work of Art, Date of creation, Institution and city where the work is
housed. Name of Website, Medium of publication, Date of access.
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